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Theses

Estimation asymptotiquement exacte en norme sup de fonctions multidimensionnelles

Abstract : We study two statistics models: the regression model with random design and the Gaussian white noise model. In these models, the goal is to estimate in sup-norm an unknown function f, from the observations, supposing that f belongs to a Holder class. In the regression model, for the estimation of a one-dimensional function, we obtain the exact constant and an asymptotically exact estimator. In the Gaussian white noise model, we study the estimation on two classes of multidimensional anisotropic functions, which one is an additive class. For these two classes, we determine the exact constant and an asymptotically exact estimator, and we show the link with "optimal recovery". The last chapter give results of exact asymptotic in an adaptative framework in the Gaussian white noise model. We determine the exact adaptive constant and an asymptotically exact adaptive estimator for the estimation on anisotropic classes.
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https://tel.archives-ouvertes.fr/tel-00008028
Contributor : Karine Bertin <>
Submitted on : Wednesday, January 12, 2005 - 5:55:40 PM
Last modification on : Wednesday, December 9, 2020 - 3:04:58 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:39:15 PM

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  • HAL Id : tel-00008028, version 1

Citation

Karine Bertin. Estimation asymptotiquement exacte en norme sup de fonctions multidimensionnelles. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00008028⟩

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